This talk reviews experimental results of the ATLAS and CMS collaborations at the LHC, comprising SM, Top and Higgs measurements

In this talk, I aim to review the phenomenology of LHC observables, related to processes newly implemented in the NNLOJET parton level event generator.

Recently, there has been significant progress in computing scattering amplitudes in the high-energy limit using rapidity evolution equations. I describe the state-of-the-art and demonstrate the interplay between exponentiation of high-energy logarithms and that of infrared singularities.

The focus in this talk is the imaginary part of 2 to 2 partonic amplitudes, which can be determined by...

We consider the extension of the CMW soft-gluon effective coupling beyond the next-to-leading logarithmic accuracy. We present two proposals of a soft-gluon effective coupling that extend the CMW coupling to all perturbative orders. Although both effective couplings are well-defined in four dimensions, we examine their behaviour in d=4-2epsilon dimensions. We uncover an all-order perturbative...

I present the complete results of "Torino" local analytic subtraction of infrared divergences from final state real radiation at NNLO in QCD and report the progresses for the analogous treatment of the radiation from the initial state.

We discuss nonfactorizable QCD corrections to Higgs boson production in vector boson fusion at the Large Hadron Collider. We point out that these corrections can be computed in the eikonal approximation retaining all the terms that are not suppressed by the ratio of the transverse momenta of the tagging jets to the total center-of-mass energy. Our analysis shows that in certain kinematic...

I will discuss Feynman integrals, which are associated to elliptic curves and their differential equations. I will show for non-trivial examples how the system of differential equations can be brought into an $\varepsilon$-form. Single-scale and multi-scale cases will be discussed.

As the experimental precision at the LHC keeps improving,

next-to-next-to leading order (NNLO) corrections for scattering processes have become crucial for providing theoretical predictions of comparable accuracy. At present, only observables involving up to four particles are available at this order. The main bottleneck towards higher multiplicity observables is the analytic calculation of...

I will talk about the recent computation of three loop jet functions (arXiv:1805.02637) in perturbative QCD. These results have been extracted from the known three loop coefficient functions for deep-inelastic scattering via the exchange of a virtual photon that couples to quarks or a scalar that couples to gluons and employing renormalization group invariance and factorization theorem. We...

Fiducial differential cross sections are reliable observables that the LHC is providing more and more precise measurements. From the theory point of view, event generators could simulate the underlying processes and apply the same experimental selection criterion to reduce the systematical errors when comparing with data. I will introduce some of the implementations and simulations from...

In this talk I will discuss new algorithmic approaches to reduce Feynman integrals. Syzygies derived in the Lee-Pomeransky and the Baikov representation allow to find linear relations, which avoid the introduction of either irreducible numerators or higher powers of propagators, respectively. The relevant syzygies can be calculated with linear algebra methods based on finite fields. These...

We present the analytic form of all two-loop five-parton helicity amplitudes required for the calculation of NNLO QCD corrections to the production of three jets at hadron colliders in the leading-color approximation. The results are analytically reconstructed from exact numerical evaluations over finite fields. We employ a number of physics-motivated ideas to facilitate the reconstruction, as...

In this talk, we outline the computational details to obtain mixed EW-QCD corrections to on-shell production of a single vector boson at the LHC at two-loop level. We use the novel method of differential equation to obtain the pure virtual, real-virtual and double-real master integrals.

In this talk, we present a detailed study on the infrared structure of N=4 SYM and its connection to QCD. Calculation of collinear splitting functions helps to understand the structure and thus one can get infrared safe cross sections. We also demonstrate the factorization property that soft plus virtual part of the cross section satisfies and through factorization, we calculate soft...

When computing perturbative corrections to a process QCD provides the phenomenologically most significant contribution. Nevertheless, because of the similar size of $\alpha_S^2$ respect to $\alpha_{QED}$, for a precision prediction one needs to consider electroweak corrections as well.

In this talk we show how one can obtain the mixed QCDxQED corrections from pure QCD NNLO corrections by...

Precise predictions for total and differential cross sections

at hadron colliders became an important corner stone of the LHC physics.

The lack of new 'smoking-gun' physics signals

requires precise comparisons between measurements and Standard Model

predictions to get a

handle on new physics effects. Tremendous efforts have been made to push

perturbative calculations to higher orders...

qT subtraction represents a well established and successful formalism to deal with the computation of QCD radiative corrections up to NNLO (and beyond) for a large class of processes relevant at the LHC. We have explored the possibility to extend qT subtraction to the computation of EW corrections with the (final) aim to develop a subtraction formalism suitable for the computation of mixed...

We discuss the relation between the infrared singularities of on-shell partonic form factors and parton distribution functions (PDFs) near the elastic limit, through their factorisation in terms of Wilson-line correlators. Ultimately we identify the difference between the anomalous dimension controlling single poles of these two quantities to all loops in terms of the closed parallelogram...

I will present the calculation of and results for the two-loop penguin amplitudes appearing in non-leptonic B-decays in the framework of QCD Factorisation. I will discuss the details of the computation of this genuine two-loop, two-scale problem, focusing i) on the analytic computation of the master integrals and ii) on the (partially analytic) convolution of the hard kernel with the...

The inclusive radiative decay of the B meson is known to provide strong constraints on new particles and their interactions. The current experimental world average for its branching ratio is $(3.32 \pm 0.15) \cdot 10^{-4}$ which agrees within one sigma with the present SM prediction $(3.36 \pm 0.23) \cdot 10^{-4}$. Some of the NNLO QCD corrections are included with the help of interpolation in...

In QCD, soft radiation plays an important role in kinematic regions where resulting threshold logarithms become large. In this talk, I address such effects beyond leading power in the threshold expansion, for both fixed order and resummed results. For the double-real single-virtual correction to Drell-Yan, a large class of next-to-leading power (NLP) threshold logarithms is shown

to be...

Independent Measurements of Higgs self-couplings are crucial to probe new physics effects in the Higgs sector. Gluon fusion is the dominant mode for double Higgs production at hadron colliders. At leading order it is sensitive to the trilinear Higgs self-coupling. At higher orders in electroweak theory, it also becomes sensitive to the quartic coupling. We present a sensitivity study on the...

We show how anomalous trilinear Higgs boson couplings, as well as other anomalous couplings in the Higgs sector, impact the shapes of distributions in Higgs boson pair production. In particular we discuss the interplay between higher order QCD corrections and effects from physics beyond the Standard Model, parametrized by Effective Field Theory. We present new methods, partly based on machine...

The expected experimental precision of the rates and asymmetries

in the Future Circular Collider with electron positron beams (FCC-ee)

in the energy range 88-365GeV considered for construction in CERN,

will be better by a factor 5-200.

This will be thanks to very high luminosity,

factor up to $10^5$ higher than in the past LEP experiments.

This poses the extraordinary challenge of...

We present NNLO QCD corrections to production of pair of

Higgs bosons in bottom quark annihilation at the Large Hadron Collider.

We take into account all the partonic channels in five flavour scheme.

We find that these corrections are important for the reliable predictions

which are less sensitive to unphysical scales.

It is known that one-loop Feynman integrals possess an algebraic structure encoding their analytic properties called the coaction, which can be written in terms of Feynman integrals and their cuts. This diagrammatic coaction, and the coaction on other classes of integrals such as hypergeometric functions, may be expressed using suitable bases of differential forms and integration contours....

A well-known result states that operators that vanish by the classical equation of motion do not mix into physical operators. The result guarantees that the S-matrix is invariant under large classes of field redefinitions. It is shown that (and why) the theorem is violated in soft-collinear effective theory beyond the leading power in the soft-collinear expansion. The mixing of eom operators...

When finding linear relations between Feynman integrals using integration-by-parts identities, a very large linear system has to be solved as an intermediate step.

This makes other approaches to the derivation of these identities a worthwhile pursuit. In this context, the concept of the intersection number is of interest, as it allows for the definition of (what amounts to) a scalar product...

In this talk, I am going to report on the resummation of the leading logarithmic corrections for the Drell-Yan production and Higgs production in gluon fusion at the next-to-leading power in threshold expansion. I will describe how the kinematic power-corrections are accounted for and the structure of renormalisation group equations for the generalised soft function which appears after...

Recent results concerning Higgs- and Z-boson decay rate

in order alpha**4 and the five-loop beta-function are presented.

We present new results for heavy quark form factors at three loop order.

We compute the third-post-Minkowskian conservative Hamiltonian of binary black holes using modern tools from scattering amplitudes and effective field theory. In the limit of large separation, non-spinning black holes have an effective description in terms scalar field particles coupled to gravity. The two-loop integrand is constructed using generalized unitarity and the double copy...

In this talk, we discuss our ongoing calculation of the four-loop form factors of massless QCD. In particular, we present results for the quark and gluon form factors which we have calculated for the first time using novel computational techniques.

Higher-order corrections to the interaction potential between non-relativistic massive objects can be obtained systematically in a Post-Newtonian expansion in the small velocity and weak coupling. We present the calculation of these corrections up to five loops using techniques from multi-loop computations in high-energy physics.

Elastic neutrino-electron scattering provides an important tool for normalizing neutrino flux in modern experiments. This process is subject to large radiative corrections. We determine the Fermi effective theory performing the one-loop matching to the Standard model at the electroweak scale with subsequent running down to GeV scale. Based on this theory, we analytically evaluate virtual...

I will present NLO corrections to Higgs boson production in association with a jet, retaining the full dependence on the top quark mass. Details of the calculation will be presented, focusing on the evaluation of the two-loop integrals, which is done numerically with the program SedDec. In particular I will present various improvements to the code, which have been achieved since the first...

The B-meson distribution amplitude is defined by the matrix element of a heavy-light quark operator between the vacuum and B-meson states. The scale dependence of the corresponding DA is governed by the renormalization group equation for this operator. At one loop the corresponding evolution kernel was derived by Lange and Neubert. I'll argue that the form of the kernel is strongly restricted...

We present the analytic calculation of the Master Integrals for certain two-loop, non-planar topologies that enter the calculation of the amplitude for top-quark pair hadroproduction in the quark-annihilation channel. These Master Integrals are needed to complete the evaluation of the two color factors in the quark-annihilation channel which are not yet known analytically at two-loop. We...

In this talk, I will present the analytic calculation of the planar master integrals for the two-loop light-fermion electroweak corrections for the production of a Higgs boson in the gluon-gluon fusion channel. The complete dependence on the electroweak boson mass is retained. The master integrals are evaluated by means of the differential equations method and the analytic result are expressed...

Within finite-temperature quantum field theory, the evaluation of vacuum-type sum-integrals plays a central role in the determination of equilibrium observables, such as the free energy (or pressure) of a thermal system.

As has been repeatedly observed in the past, many two-loop sum-integrals can be decomposed into one-loop factors, allowing for analytic solutions in the space-time dimension...

Soft Collinear Effective Theory (SCET) formalism has been successfully applied to a number of important observables in collider physics improving the accuracy of fixed-order predictions via the leading power resummation of large logarithmic contributions which appear in certain regions of phase space. Recently, a renewed interest in subleading power corrections has arisen in the theoretical...

Recently, we have worked out how thousands of moments of Feynman integrals can be computed if they are represented by coupled systems of linear differential equations and sufficiently many initial values. Given these moments one is in the position to derive recurrence relations and to solve these recurrences, e.g., within the class of indefinite nested sums. In this talk we will present a...

With the goal of increasing the precision of NLO QCD predictions for the pp->ttγ process in the di-lepton top quark decay channel we present theoretical predictions for the cross section ratio. Results for the latter together with various differential cross section ratios will be presented for the LHC Run II energy of 13 TeV. Fully realistic NLO QCD computations for both tt and ttγ production...

Gluon fusion processes like single and double Higgs production exhibit slow convergence and pose severe computational challenges. We show how the top-quark mass dependence of the virtual amplitudes can be reconstructed with a conformal mapping and Padé approximants based on the expansion in the inverse top-quark mass and the non-analytic terms in the expansion around the top threshold. The...

Within the framework of the standard model as well as the two Higgs

doublet model including the MSSM as a special case, we examine the

CP-even and CP-odd Higgs boson production in electron-photon collisions.

We particularly emphasize the role of the transition form factor

in terms of which the production amplitudes can be given.

Relating loop integrals to tree level objects goes back several decades to Feynman. In the past ten years the loop-tree duality theorem was introduced, which expresses $l$-loop integrals in terms of phase space integrals of sum of trees obtained from cutting $l$ internal propagators of the loop graph. In addition, the uncut propagators gain a modified $i \delta$-prescription, named dual...

In this talk, we discuss top quark contributions to ZZ production through gluon fusion at two loops. We use a syzygy based approach for the reductions to master integrals. In order to numerically evaluate the amplitude, we express it in terms of finite integrals, which we construct out of linear combinations of divergent integrals using a new algorithm.

In order to make predictions that can be compared with the results that the LHC delivers, there are several approaches to compare the experiment with the theory. It is known that to establish this comparison, we cannot rely on leading order (LO) calculations only. Hence, we need to consider next-to-leading order (NLO) contributions, that are often understood as virtual and real. Although we...

We compute the two-loop massless QCD corrections to the four point amplitude

g + g -> A + A. Two operators contribute this amplitude and the ultraviolet renormalisation requires careful treatment involving mixing. The universal structure of the infrared poles are studied in detail.

I discuss the latest developments of FDR in the context of Quantum Field Theory calculations relevant for High Energy Physics phenomenology. In particular, I focus on NNLO computations and the use of FDR in connection to effective QFTs.

Productions of the Higgs boson in association with a massive vector boson, i.e. the VH events, play an important role in the explorations of Higgs physics at the LHC, both for a precise study of Higgs' Standard Model couplings and for probing new physics. In this talk, we present the 2-loop massless QCD corrections to the helicity amplitudes of the associated Higgs production through the...

The proper renormalization of mixing angles in quantum field theories

is a long-standing problem. It is relevant for the renormalization of the

quark mixing matrix in the Standard Model and for various mixing

scenarios in theories beyond. In this talk we specifically consider

theories with extended scalar sectors. We review existing renormalization

schemes for mixing angles and introduce...

In this talk, I present the computation of the two loop massless QCD corrections to the four-point amplitude $g + g → H + H$ (arXiv:1809.05388) resulting from effective operator insertions that describe the interaction of a Higgs boson with gluons in the infinite top quark mass limit. This amplitude is an essential ingredient to the third-order QCD corrections to Higgs boson pair production....

The consistent recursive subtraction of UV divergences order by order in the loop expansion for spontaneously broken effective gauge theories with higher dimension derivative operators is presented. The Slavnov-Taylor identity is solved to all orders in the loop expansion by homotopy techniques and a suitable choice of invariant field coordinates (named bleached variables) for the linearly...

Recent results are presented on polarized and unpolarized heavy flavor corrections

to DIS to 2- and 3-loop order in the full region and for large virtualities.

In the polarized case we also discuss the treatment of \gamma_5 and derive

results in the M-scheme.

KKMC-hh is a precision event generator for Z boson production at a hadron collider, based on coherent exclusive exponentiation (CEEX) of soft photon emission at the amplitude level. We will summarize studies of ISR and IFI effects on calculations AFB for precision EW analysis at the LHC. Different approaches to ISR will be compared, and progress will be reported on implementing NLO QCD in KKMC-hh.

Our renormalization group consistent version of optimized perturbation, RGOPT, had been used to calculate the nonperturbative QCD spectral density of the Dirac operator and the related chiral quark condensate $\langle \bar q q \rangle$, for $n_f=2$ and $n_f=3$ massless quarks. Sequences of approximations at two-, three-, and four-loop orders gave stable parameter-free determinations...

In this talk I will present open issues in the deacription of processes leading to the hadroproduction of at least one heavy meson or baryon, considering different flavour number schemes. Solving these issues is important for improving the accuracy of PDf fits and of predictions in high-energy astroparticle physics.

IR-improvement based on amplitude-level resummation allows one to control unintegrable results in quantum field theory with arbitrary precision in principle. We illustrate such resummation in specific examples in precision LHC and FCC physics and in quantum gravity.

Feynman integrals that have been evaluated in dimensional regularization can be written in terms of generalized hypergeometric functions. It is well known that properties of these functions are revealed in the framework of intersection theory. We propose further applications of intersection theory in the case of functions associated to positive geometries, in particular to construct a...

In this talk we discuss NNLO and N3LO order corrections

to the process gg->HH in the Standard Model. In particular,

we consider three-loop corrections to the form factors entering the virtual

corrections in the large-mt

limit and compute five expansion terms.

In the same approximation we also evaluate the

real radiation corrections at NNLO. Finally, we present

a building block for the...

The cusp anomalous dimension is a universal and ubiquitous quantity in QCD. It governs the IR structure of scattering amplitudes and is the key ingredient to (Sudakov) resummation for high-energy collider processes. I will report on recent analytic results on the matter dependence of the cusp anomalous dimension at four loops and discuss the calculational methods used to obtain them.

We present a fully-differential calculation of the $H \to b\overline{b}$ decay at next-to-next-to-next-to-leading order (N3LO) accuracy. Our calculation considers diagrams in which the Higgs boson couples directly to the bottom quarks. In order to regulate the infrared divergences present at this order we use the Projection-to-Born technique coupled with N-jettiness slicing. After validating...

We present a calculation of the NLO QCD corrections to the loop-induced production of a photon pair through gluon fusion, including massive top quarks at two loops, where the two-loop integrals are calculated numerically. Matching the results for the virtual amplitude to a threshold expansion, we obtain accurate results around the top quark pair production threshold. We analyse how the top...

I this talk I will show the result of the 1100-digits calculation of the 4-loop QED contribution to the first derivative of the Dirac form factor at zero momentum transfer. An analytical fit has been obtained, and I will describe its structure. I will discuss also the contribution of this result to the Lamb shift of hydrogen.